Yi Mao
Dept. of Phys. and Astron., Univ. of Mississippi, University, MS 38677
Lawrence A. Crum Ronald A. Roy
Univ. of Washington, Seattle, WA 98105
The second resonance frequency f[sub 0][sup (2)] of a pure bubble appeared first in R. D. Finch and E. A. Nippiras' theoretical analysis [J. Acoust. Soc. Am. 53, 1402--1410 (1973)]. However, no one has been able to observe a vapor bubble oscillating at f[sub 0][sup (2)]. A new analysis based on numerical calculations shows that f[sub 0][sup (2)] is physically unstable. By analogizing bubble oscillations with those of a mass-spring system, it is found that the resonance frequency F(f[sub d]) depends on the driving frequency f[sub d] and the real bubble resonance f[sub 0][sup (2)] is a solution of F(f[sub d])=f[sub d]. The behavior of F(f[sub d]) near f[sub d]=f[sub 0][sup (2)] shows that the bubble tends to shift its oscillation frequency away from f[sub 0][sup (2)] (repulsive); whereas F(f[sub d]) near the ordinary resonance f[sub 0][sup (1)] is attractive. A theory developed by the authors for directly calculating the resonance frequency and the damping constant without using the mass-spring analogy gives only f[sub 0][sup (1)]. Therefore, we are forced to the conclusion that f[sub 0][sup (2)] results from an improper mass-spring analogy and is not physically observable. [Work supported by ONR.]